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arXiv 2303.14529math.HOmath.LO
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时间真理与二价--对亚里士多德《解释论》的一种时代错误的形式分析

Temporal truth and bivalence an anachronistic formal approach to Aristotle's De Interpretatione 9

Luiz Henrique Lopes dos Santos

摘要:

关于亚里士多德在《解释论》第9章中提出的著名的海战论证,人们不仅对它的正确性,而且主要是对这个论证到底是什么,从来没有达成普遍的一致意见。根据对本章最自然的解读,论证诉诸于真理的时间概念,并得出结论,并非每一个陈述总是真或假。然而,亚里士多德的许多追随者和评论家并没有采用这种解读。我相信,由于解释学上的仁慈,它面临着如此多的阻力,否认普遍二价律似乎对逻辑正统具有过度的破坏性,这种逻辑正统由我们现在所说的经典命题逻辑所代表,其中大部分亚里士多德在许多文本中明确支持。我打算表明,传统阅读在《解释论》第9章中发现的逻辑语义命题比乍看上去要保守得多。首先,我将表明,它们补充了亚里士多德在其他文本中提出的真理和陈述概念的正统定义,而不是以任何方式相矛盾。第二,通过诉诸于一个不合时宜的静脉的概念和方法特有的当代逻辑,我将表明,三价模态语义符合这些论文可以建立一个标准的形式语言的经典命题演算。值得注意的是,可以在这种三价模态语义学的基础上定义的逻辑真值和逻辑推论的合理概念与它们的正统对应物,经典二价和外延语义学的重言式和重言式推论的概念是同延的。

英文摘要:

Regarding the famous Sea Battle Argument, which Aristotle presents in De Interpretatione 9, there has never been a general agreement not only about its correctness but also, and mainly, about what the argument really is. According to the most natural reading of the chapter, the argument appeals to a temporal concept of truth and concludes that not every statement is always either true or false. However, many of Aristotle's followers and commentators have not adopted this reading. I believe that it has faced so much resistance for reasons of hermeneutic charity denying the law of universal bivalence seems to be overly disruptive to logical orthodoxy the kind of logical orthodoxy represented by what we now call classical propositional logic, much of which Aristotle clearly supports in many texts. I intend to show that the logical-semantic theses that the traditional reading finds in De Interpretatione 9 are much more conservative than they may seem to be at first glance. First, I will show that they complement, and do not contradict in any way, the orthodox definitions of the concepts of truth and statement that Aristotle advances in other texts. Second, by resorting in an anachronistic vein to concepts and methods peculiar to contemporary logic, I will show that a trivalent modal semantics conforming to those theses can be built for a standard formal language of the classical propositional calculus. It is remarkable that reasonable concepts of logical truth and logical consequence that may be defined on the basis of this trivalent modal semantics are coextensive with their orthodox counterparts, the concepts of tautology and tautological consequence of classical bivalent and extensional semantics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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